Stochastic filtering of approximate symmetries in dense packings of clusters

摘要

Certain questions concerning the arrangement of optimal dense packings of clusters are considered when simple routine long-term procedures are applied instead of a laborious method of direct solution. A unified approach to searching for hidden symmetries in such packings is proposed that represents a certain combination of the generalized Hough transform and the Purzen windows technique in nonparametric density estimation. All symmetries are sought via the Hough transforms adjusted to certain types of adjacent classes on the SO N group manifold. Exact symmetries and separate solutions are filtered out by using the ergodic properties of the independent sequential choice procedure.